The ends of a stretched wire of length L are fixed at x $$=$$ $$0$$ and x $$=$$ L. In one experiment, the displacement of the wire is $$y1=Asin($$π$$x/L)$$$$sin$$ωt and energy is $$E1$$, and in another experiment its displacement is $$y2=Asin(2$$$$π$$$$x/L)sin2$$ωt and energy is $$E2$$. Then

Question

The ends of a stretched wire of length L are fixed at x $$=$$ $$0$$ and x $$=$$ L. In one experiment, the displacement of the wire is $$y1=Asin($$π$$x/L)$$$$sin$$ωt and energy is $$E1$$, and in another experiment its displacement is $$y2=Asin(2$$$$π$$$$x/L)sin2$$ωt and energy is $$E2$$. Then

Infinity Learn · Accepted Answer

Energy (E) ∝ (Amplitude)2$$ $$(Frequency)2$$ Amplitude is same in both the cases, but frequency $$2$$ ω in the second case is two times the frequency $$($$ω$$) in the first case. Hence $$E2=4E1$$.

The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the displacement of the wire is $y_{1} = Asin (πx / L) sinωt$ and energy is E₁, and in another experiment its displacement is $y_{2} = Asin (2 πx / L) \sin 2 ωt$ and energy is E₂. Then

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The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the displacement of the wire is y1=Asin(πx/L)sinωt and energy is E1, and in another experiment its displacement is y2=Asin(2πx/L)sin2ωt and energy is E2. Then

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Ready to Test Your Skills?

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The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the displacement of the wire is $y_{1} = Asin (πx / L) sinωt$ and energy is E₁, and in another experiment its displacement is $y_{2} = Asin (2 πx / L) \sin 2 ωt$ and energy is E₂. Then